Photonic memory devices are capable of giving different outputs for the same present input, judging from the input’s past values and, in this way, “remembering” what happened the previous times. Nonlinear cylindrical metasurfaces, when fed centrally by line sources of various angular momenta, are found to possess exactly this property, which is called multistability; in particular, they can develop multiple responses in proportion to what the history of excitation intensities is. Interestingly, some of the potential radiation patterns of the considered nanotubes, despite the homogeneous and isotropic nature of the structure, are azimuthally rotated, even for symmetric excitations. Such a feature of several alternative stable solutions with different amplitudes and angular tilts may provide a promising route for designing reconfigurable optical setups with versatile memory and storage utilities.